The propagation of an intense (a₀ = 3), short-pulse (L ~l _p) laser through a homogeneous plasma has been investigated. Using two-dimensional simulations for a₀ =3, the pulse-length and spot-size at three different plasma densities were optimized in order to get a better quality beam in laser wakefield accelerator. The study reveals that with increasing pulse-length the acceleration increases, but after a certain pulse-length (L > 0.23 l_p) the emittance blows-up unacceptably. For spot-sizes less than that given by kp_0rs =2 a₀, trapping is poor or nonexistent, and the optimal spot-size is larger. The deviation of the optimal spot-size from this formula increases as the density decreases. The efficacy of these two-dimensional simulations has been validated by running three-dimensional simulations at the highest density. It has been shown that good quality GeV-class beams can be obtained at plasma densities of ~ 10¹⁸cm^-3. The quality of the beam can be substantially improved by selecting only the high-energy peak.; in this fashion an energy-spread of better than 1% and a current in tens of kA can be achieved, which are important for applications such as free-electron lasers.